BANG-BANG THEOREM WITH BOUNDS ON THE NUMBER OF SWITCHINGS.

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Abstract

For systems of the form dx/dt equals f(x) plus ug(x), with f and g analytic, and minus 1 less than equivalent to u less than equivalent to 1, there is proved a bang-bang theorem with a priori bounds on the number of switchings, provided that the following condition is satisfied: in a neighborhood of every point x, it is possible to express, for each j, the vector field left bracket g, (ad f)**i(g) right bracket as a linear combination of the (ad f)**i(g), i less than equivalent to j plus 1, in such a way that the coefficient of (ad f)**j** plus **1(g) in this expression is bounded in absolute value by a constant c less than 1.

Original languageEnglish (US)
Pages (from-to)629-651
Number of pages23
JournalSIAM Journal on Control and Optimization
Volume17
Issue number5
DOIs
StatePublished - 1979

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

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